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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h2>Bayesian Inference of the mean of a Gaussian</h2>\n",
      "<p>In this notebook, we will use Bayesian inference to infer the mean of a Gaussian. We assume that we observe $N$ values that have come from a Gaussian with mean $\\mu$ and variancs $\\sigma^2$. Assuming that we know $\\sigma^2=1$, we would like to determine $\\mu$.</p>\n",
      "\n",
      "<p>We start by defining a prior density on $\\mu$. We will use a Gaussian as our likelihood will be Gaussian (as per our assumption above) and the Gaussian prior is conjugate to the Gaussian likelihood. We (arbitrarily - in real problems you should think carefully about prior values) choose a prior with mean $a=0$ and variance $b^2=1$</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "true_mu = 2.0\n",
      "a = 0\n",
      "b_sq = 1\n",
      "sig_sq = 1\n",
      "x = np.random.normal(true_mu,np.sqrt(sig_sq),(10,1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>The plot below shows our choice of prior density:</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab as plt\n",
      "%matplotlib inline\n",
      "\n",
      "def normal_pdf(x,mu,sigma):\n",
      "    return (1.0/(sigma*np.sqrt(2*np.pi)))*np.exp(-(1.0/(2.0*sigma**2))*(x-mu)**2)\n",
      "\n",
      "plotx = np.arange(-5,5,0.01)\n",
      "plt.plot(plotx,normal_pdf(plotx,a,np.sqrt(b_sq)),'r')\n",
      "plt.title('Prior density')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "<matplotlib.text.Text at 0x113551690>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11399f510>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>We now add the data one at a time, and see how the posterior density changes. In the plots, the red curve is the prior, the blue curve the posterior and the black circles the data.</p>\n",
      "\n",
      "<p>Because we chose a conjugate prior-likelihood pair, we are able to compute the posterior analytically. We know it must be Gaussian and...to be finished</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "all_c = []\n",
      "all_d_sq = []\n",
      "for i in np.arange(x.size):\n",
      "    d_sq = 1.0/(1.0/b_sq + (i+1.0)/sig_sq)\n",
      "    c = d_sq*(a/b_sq + x[0:i+1].sum()/sig_sq)\n",
      "    all_c.append(c)\n",
      "    all_d_sq.append(d_sq)\n",
      "    plt.figure()\n",
      "    plt.plot(plotx,normal_pdf(plotx,a,np.sqrt(b)),'r')\n",
      "    plt.plot(plotx,normal_pdf(plotx,c,np.sqrt(d_sq)),'b')\n",
      "    plt.plot(x[0:i+1],np.zeros_like(x[0:i+1]),'ko',markersize=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mxJFvRdMrZqN1Pd9C7ek2JvLLL/DQQ8badu8e/stgYyiOPBnNqNgD1fhctOSb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\n7Wh1HRQnwcXuTQ0CF5UATbo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ZmZn07t07fOOyjZGkWVvQqkDe2q6LxpSXfY4d05QQS5ZA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\nxsbGxsbGxsbGxsbGxsbGxsYK/h8F615fIHKTFgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113a00750>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(np.arange(x.size)+1,all_c,'k')\n",
      "plt.plot([1,x.size+1],[true_mu,true_mu],'k--')\n",
      "plt.xlabel('N')\n",
      "plt.ylabel('c')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "<matplotlib.text.Text at 0x1138a0910>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aWJaopkAQqZvyJ/9ncNA950VEREREREREREREREREREREREREREREREREREQC\n8v/Ee/wbcGPd9QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1138bda90>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(np.arange(x.size)+1,all_d_sq,'r')\n",
      "plt.xlabel('N')\n",
      "plt.ylabel('$d^2$')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "<matplotlib.text.Text at 0x113199490>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oCzXcVF1JkiRJkiRJkiRJkiRJkiQpRZqTDkBqAO2E9Q/zosfXEhZnzk8sIqmH\nXGEuVd+7hNXEA6PHHQnGIvUKk4dUfduAHwB/l3QgUm8xeUjxuJ1wVdd9kg5E6g0mDykemwlXCk7D\n9qxSj5k8pPjcCnyecBFBqaaZPKT4vA38hJBAbJqrppk8pOrLTxQ3E/ZUkSRJkiRJkiRJkiRJkiRJ\nkiRJkiRJkuL3/wGm8pzLC7lgvgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11355a150>"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}